- From: Stefan Eissing <stefan.eissing@greenbytes.de>
- Date: Thu, 29 Aug 2002 18:05:43 +0200
- To: Tim Bray <tbray@textuality.com>
- Cc: Jeff Bone <jbone@deepfile.com>, "Roy T. Fielding" <fielding@apache.org>, Norman Walsh <Norman.Walsh@Sun.COM>, www-tag@w3.org
Am Donnerstag den, 29. August 2002, um 17:30, schrieb Tim Bray: > > Jeff Bone wrote: > >> Tim, I buy your argument. But the problem then is that it >> implies that URI cannot represent the reals. A proper subset of >> a denumerable set cannot stand in one-to-one correspondance with >> a non-denumerable set, right? OTOH, it seems to me that, for any >> given real number, it is possible to construct a (or many - >> perhaps infinitely many) URIs that can stand for that real >> number... > > Er well my math degree is dated 1981, so the intuition is somewhat > rusty. I believe, when you come right down to it, that the > problem is that there are lots of reals that have no names. > Clearly I could write URIs for well-known irrationals like e, pi, > and their friends. It is obvious that there is no finite > representation of an irrational using a positional numeric > notation. So unless you have some other way of getting at it > (ratio between circumference and diameter, integral of 1/x, square > root of 2) you'll never get a name, which means that it just isn't > a resource (a thing that has identity), so the world-view is kind > of consistent. Well, you can give *any* real number a name, but you cannot give *every* real number a name. (The amount of information represented by the set of real numbers is greater than the amount of information represented by an infinite set of finite words formed from a finite alphabet.) > > Think of all those poor nameless reals... that's a special kind of > loneliness. -Tim I donate a URI from http://greenbytes.de/ for the first number you do not give one. Or, look at the positive side: the amount of possible future top level domains is numerable! //Stefan
Received on Thursday, 29 August 2002 12:06:45 UTC